Image segmentation with a finite element method
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Blaise Bourdin (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Blaise Bourdin (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
The Mumford-Shah functional for image segmentation is an original approach of the image segmentation problem, based on a minimal energy criterion. Its minimization can be seen as a free discontinuity problem and is based on Γ-convergence and bounded variation functions theories. Some new regularization results, make possible to imagine a finite element resolution method. In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation...
J. Sivaloganathan (1988)
Annales de l'I.H.P. Analyse non linéaire
Szymon Dolecki, Maria-Pia Moschen (1987)
Rendiconti del Seminario Matematico della Università di Padova
Ennio De Giorgi, Luigi Ambrosio, Giuseppe Buttazzo (1987)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Given a separable metric locally compact space , and a positive finite non-atomic measure on , we study the integral representation on the space of measures with bounded variation of the lower semicontinuous envelope of the functional with respect to the weak convergence of measures.
Guy Bouchitté, Gianni Dal Maso (1993)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Alessandra Coscia, Domenico Mucci (2002)
ESAIM: Control, Optimisation and Calculus of Variations
We study the integral representation properties of limits of sequences of integral functionals like under nonstandard growth conditions of -type: namely, we assume thatUnder weak assumptions on the continuous function , we prove -convergence to integral functionals of the same type. We also analyse the case of integrands depending explicitly on ; finally we weaken the assumption allowing to be discontinuous on nice sets.
Alessandra Coscia, Domenico Mucci (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We study the integral representation properties of limits of sequences of integral functionals like under nonstandard growth conditions of (p,q)-type: namely, we assume that Under weak assumptions on the continuous function p(x), we prove Γ-convergence to integral functionals of the same type. We also analyse the case of integrands f(x,u,Du) depending explicitly on u; finally we weaken the assumption allowing p(x) to be discontinuous on nice sets.
G. Bouchitté, G. Buttazzo (1992)
Annales de l'I.H.P. Analyse non linéaire
Gianni Dal Maso (1979/1980)
Manuscripta mathematica
Michele Carriero, Antonio Leaci, Eduardo Pascali (1985)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Diamo condizioni sulle funzioni , e sulla misura affinché il funzionale sia -semicontinuo inferiormente su . Affrontiamo successivamente il problema del rilassamento.
Stefan Hildebrandt (1973)
Mathematische Zeitschrift
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